The graph of the line $x+y=b$ intersects the line segment from $(2,5)$ to $(4,9)$ at its midpoint. What is the value of $b$?
Explanation: If the line $x+y=b$ intersects the midpoint, which is: $$\left(\frac{2+4}{2},\frac{5+9}{2}\right)=(3,7)$$This point lies on the line $x+y=b$, so we must have $3+7=b$. Thus, $b=\boxed{10}$.